S-wave conversion in marine surveys

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Problem 13.1a

In a marine survey, the water depth is 100 m and a reflector is 3 km below the seafloor. Use Figure 13.1a to determine the optimum range of offsets for S-wave generation. Take Poisson’s ratio just below the seafloor as 0.35 and the P-wave velocity as 2.8 km/s. The velocity in sea water is 1.5 km/s.


Referring to Figure 13.1a(i), we see that the offset for the 3-km reflector is


where is the angle of incidence of the P-wave at the bottom of the water layer, and is the angle of refraction of the converted S-wave.

To find for a given , we need the S-wave velocity . Using equation (1,8) in Table 2.2a, we find that for , so . To get the angles of incidence and of refraction , we have from equation (3.1a),

Figure 13.1a.  PSSP reflections generated by conversion at the sea floor (after Tatham and Stoffa, 1976). (i) Geometry; (ii) the conversion coefficient versus angle of incidence in the water; the curves are labeled with the seafloor P-wave velocity in km/s. [Note: Conversion coefficient = (amplitude of converted wave/amplitude of incident wave.)

The optimum angles of incidence for S-wave conversion for are obtained by interpolating between the curves for and 3.0 in Figure 13.1a(ii). This gives a range of about to for . The corresponding values of are and . Equation (13.1a) now gives offsets of 4 and 11 km for and .

Problem 13.1b

Most marine S-wave surveys that wish to deal with S-waves utilize conversion at the reflector and recording with three-component geophones laid on the seafloor (OBC, ocean-bottom cables), so that only one mode conversion is involved. Assume a ray leaving an airgun source at to the vertical in water 100 m deep, an increase in P-wave velocities from 1.5 km/s at the seafloor to 3.0 km/s at a reflector 3 km below the sea floor (average velocity in the sediments of 2.25 km/s). Take in the sediments as 0.3. What will be the source-geophone offset?


The P-wave gives an incident angle at the reflector of . Using equation 1,8 in Table 2.2a, the S-wave velocity here is about 0.53 or 1.59 km/s. Hence the angle of reflection is . The average direction of the P-wave ray in the sediments is . With constant in the sediments, is constant and, hence, . Hence, the average direction of the S-wave is . The offset is thus

This is a very reasonable offset.

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